The value of a for which the equation 2 urr + 8 ury + a Uyy = 0 =D0 becomes Parabolic 8 16 4

Q: Consider the equation x2 + 8x² + z² = 30, then take a cross section when x = 1. Describe the…

A: 6.     Resulting shape gives two parallel line.

Q: 5x² - 7y² - 5z² = 1

A: The equation is

Q: Calculate the focus and the directrix of the parabola x^2 + 2 x y + y^2 - 4 x + 2 y - 6 = 0.

A: The given equation of conic is:To find:The focus and directrix of the given parabola.Concept:The…

Q: Find the equation of the line that is tangent to the hyperbola at the given point. Write your answer…

A:

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

Q: During one test on the car, a point on the tire has a minimum height of 30 cm, a maximum height of…

A: The sinusoidal function based on the cosine ratio is given by: h=acosb(t-c)+d here,  a - amplitudeb…

Q: 1. A parabola has equation -12x + y? – 24 = 0. Write the equation in standard form.

A: The equation of the parabola is, - 12x + y² - 24 = 0 So, y² = 12x + 24

Q: Write the equation in standard form 4y2-9x2-18x-8y-41=0

A: 4y2-9x2-18x-8y-41=04y2-8y-9x2-18x-41=04y2-2y-9x2-2x=41y-129-x--124=1y-1232-x+1222=1 The equation…

Q: Find a motion that moves the line x + 2y = 3 to the y-axis and point (1,1) to the origin. Give the…

A: We need to find the motion which moves the line x+2y=3 to the y-axis and the point (1,1) to the…

Q: Find a motion that moves the line x + 2y = 3 to the y-axis and point (1, 1) to the origin. Give the…

A: To find a motion that moves the line x+2y=3 to the y-axis and the point 1,1 to the origin i.e.0,0.…

Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

A:

Q: Which equation would shift the parabola down 3 units? A y=z² B y=z² +3 C_y=(z-3)² Dy=(z+3)²³ E =…

A: which equation would shift the parabola down to 3 units.

Q: Find the equation of the following parabola. Express your answer in standard form. 20 -15 -10 -5 15…

A: The standard equation of the parabola is written in the form ofy=ax2+bx+c

Q: An object is observed travelling in a hyperbolic trajectory with the sun at one focus of the…

A: Given information:  1. Sun is one of the focus of hyperbola . 2. The Sun co-ordinate is 0,0.…

Q: State whether the equation z - ()² = (+)² defines a hyperboloid of two sheets. an ellipsoid. a…

A:

Q: Find the directrix of the parabola described by the equation 6 (x – 3) + (y + 2)? = 0 O x = } O x =…

A: The  parabola with vertex at (h,k) and focus at (h-a,k) has a standard equation, (y-k)2=-4a(x-h) The…

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: x +y +333x+444y+777 =0 3x² +2y² +12x-4y+2 = 0 9. 10.

A:

Q: help in 30mins pls

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Q: Determines the Cartesian equation of the plan that is parallel to the plan 2x - 3y + z - 1=0 and…

A: We have to find the equation that is parallel to the plane 2x-3y+z-1=0. Also plane passes through…

Q: Given the equation: 2x? + 3y? – 6x +6y = 12 Identify the conic and explain how you know.

A: Given: 2x2+3y2-6x+6y=12To identify the given conic:

Q: 2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.